Neutron-wave propagation in moderating media is investigated within the framework of the diffusion approximation to the Boltzmann equation, using a realistic scattering model and the eigenfunction expansion method. The eigenfunctions are obtained from the thermalization theory solution to the exponential experiment with their corresponding eigenvalues being the fundamental and higher diffusion lengths of the medium. Expanding the energy dependence of the neutron-wave problem in these eigenfunctions leads to a simpler and more accurate secular determinant than that obtained from a Laguerre polynomial expansion. Solving the secular determinant yields the squared complex inverse relaxation lengths for the asymptotic energy mode and for the continuum energy modes. A discrete energy formulation, Simpson's rule integration scheme, and the Jacobi method of matrix diagonalization are used in the numerical solution to the eigen-value problem. The dispersion law for graphite, obtained by direct solution of the complex secular determinant, is compared with experimental results. This investigation indicates that high-energy-mode contamination will not seriously affect neutron-wave experiments in graphite in the frequency range where diffusion and thermalization parameters can be obtained.